dy / dx = sin x / cos y
We rewrite the equation:
(cos (y) * dy) = (sin (x) * dx)
We integrate both sides of the equation:
sin (y) = - cos (x) + C
We use the initial condition to find the constant C:
sin (3pi / 2) = - cos (0) + C
-1 = -1 + C
C = -1 + 1
C = 0
The equation is then:
sin (y) = - cos (x)
Clearing y:
y = Arcosine (-cos (x))
Answer:
An equation for and in terms of x is:
y = Arcosine (-cos (x))